MUMBAI, India (CNN) -- A second Indian official offered his resignation Monday in the wake of last week's deadly terrorist attacks as Pakistan urged its nuclear neighbor to withhold blame until further investigation.

Vilasrao Deshmukh, chief minister of the state of Maharashtra where Mumbai is located, said he would leave it up to his ruling Congress party to decide whether his resignation would be accepted.

His announcement followed Sunday's resignation of federal Home Minister Shivraj Patil, who quit amid criticism of the response to Wednesday's attacks that left 179 dead.

The attacks have damaged India's already strained relationship with Pakistan, which says India has yet to offer any proof to support allegations that a Pakistani-based Islamic militant group was behind the massacre.

One captured suspect has told police that he is Pakistani, Indian officials said. Sources told CNN's sister station, CNN-IBN, that the captive has said he was trained by Lashkar-e-Tayyiba, a Pakistan-based terror group allied with al Qaeda.

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In Washington, Pakistan's ambassador to the United States said the attacks could be a chance to improve cooperation and ease "the burden of history" between the longtime South Asian rivals, who have fought three major wars since independence and conducted tit-for-tat nuclear weapons tests in 1998.

"It's important to avoid miscalculations. It's important not to ratchet up tensions. It is important to understand that this is an opportunity for India and Pakistan to work together," Ambassador Husain Haqqani told CNN's "Late Edition with Wolf Blitzer" on Sunday.

Police in Mumbai, located in Maharashtra state, on Monday revised downward the death toll from Wednesday's attacks and the sieges that followed to 179 dead and about 300 wounded.

The official death toll does not include at least nine gunmen killed in three days of battles with police and the Indian military, police said Monday.

Prime Minister Manmohan Singh accepted the resignation of Patil, the home minister, and immediately named Finance Minister P. Chidambaram to take over the post, according to a source in the prime minister's office.

Patil, whose ministry oversees internal security, had been accused of failing to improve intelligence before the attacks, said N. Ram, editor-in-chief of The Hindu, a major Indian newspaper.

"This man has been widely criticized for not being up to it and it was simply impossible that he could stay on after this," Ram said.

Indian officials allege that in the 1990s, Lashkar-e-Tayyiba was a state-sponsored terror group used by the Pakistani government to get control of the disputed northern Kashmir region. Pakistan banned the group in 2002, after an attack on India's parliament that brought the two countries to the brink of war.

The Indian government is considering suspending the five-year old cease-fire with Pakistan and perhaps even ending the dialogue process with the country, CNN-IBN reported.

Pakistani security officials also told CNN that if tensions with India escalate, it may shift its military forces from the Afghan border east to prepare for any conflict.

Pakistan's new democratic government, which took office earlier this year, is battling its own insurgency along the rugged border with Afghanistan, where U.S. and NATO troops have been fighting al Qaeda and Taliban militants since al Qaeda's 2001 attacks on New York and Washington.

Haqqani said the militants want India and Pakistan to remain "at each other's throats so they can flourish," but he said his government has seen no sign of an Indian buildup along the border.

"However, if there is any troop buildup on our eastern border, we will certainly have to take defensive positions. And, unfortunately, that may mean bringing troops from the western border," he said. "We don't want it. We know India doesn't want it. And we know that the international community doesn't want it."

U.S. President George Bush spoke to Singh on Sunday. Noting that U.S. citizens were among those killed, the president "said that we would all be working together, with the international community, to go after these extremists," according to a statement from National Security Council spokesman Gordon Johndroe.

U.S. Secretary of State Condoleezza Rice was scheduled to arrive in India on Wednesday in the wake of the attacks, the White House said.

Rice was scheduled to depart Sunday night for an already scheduled trip to London, said Press Secretary Dana Perino in a statement. Rice will attend a NATO meeting on Tuesday before traveling to India, where she is expected to arrive in New Delhi on Wednesday.

Interpol had said it would send a delegation to India to aid in the investigation. But on Sunday, the international law enforcement agency was still waiting official permission into the country, a spokesman said.

The targets of the attacks included luxury hotels packed with foreign tourists. The 105-year-old Taj Mahal hotel was the site of the attackers' final stand, as gunmen held hostages and refused to leave the facility.

The chairman of the company that owns the hotel told CNN that the company had been warned about the possibility of a terrorist attack before the massacre.

The hotel heightened security as a result, the chairman of the Tata Group and Taj Hotels, Ratan Tata, said in a taped interview with Fareed Zakaria on CNN's "GPS." There were indications, though, that the hotel relaxed security before the attack.

"It's ironic that we did have such a warning and we did have some measures," Tata said. "People couldn't park their cars in the portico where you had to go through a metal detector."

"They came from somewhere in the back. They planned everything," he said of the attackers. "I believe the first thing they did, they shot a sniffer dog and his handler. They went through the kitchen, they knew what they were doing."